Neural networks for sports betting
This is probably not going to work well as a way to make money. People with far larger budgets, and far more training, are already milking out any money to be made this way. This is probably their day job, and they are good at it.

That said, here are some ideas:


You do not need or want to use a convolutional network for this. Convolutional networks are useful when you want to detect a pattern invariant to translation in complex inputs. The only translation you have is that the teams could appear in either order. Just input them in both possible orders if this is a concern.
You want to find similar games. You do not need or (generally) want to use a neural network to do this. As a starting point, normalize the features and compute the nearest neighbors of an input point directly. Algorithms for doing this are fast and will return all similar points. You can even (with small modifications) output the degree of similarity as a numeric value.
If you want to predict who will win, you will probably have much better luck doing that directly. Build a feed-forward neural network that predicts which team won from the features you gathered. This is a routine classification task, and the resulting model will probably work better than finding similar games and then trying to manually determine what to do.
If you care about scores instead of just who won, use a feed forward network for regression instead of classification. The task is almost identical.